Neural gradients are near-lognormal: improved quantized and sparse training

Abstract

While training can mostly be accelerated by reducing the time needed to propagate neural gradients back throughout the model, most previous works focus on the quantization/pruning of weights and activations. These methods are often not applicable to neural gradients, which have very different statistical properties. Distinguished from weights and activations, we find that the distribution of neural gradients is approximately lognormal. Considering this, we suggest two closed-form analytical methods to reduce the computational and memory burdens of neural gradients. The first method optimizes the floating-point format and scale of the gradients. The second method accurately sets sparsity thresholds for gradient pruning. Each method achieves state-of-the-art results on ImageNet. To the best of our knowledge, this paper is the first to (1) quantize the gradients to 6-bit floating-point formats, or (2) achieve up to 85% gradient sparsity -- in each case without accuracy degradation. Reference implementation accompanies the paper.

References in corpus (12)

• Quantizing deep convolutional networks for efficient inference: A whitepaper
• PACT: Parameterized Clipping Activation for Quantized Neural Networks
• Training and Inference with Integers in Deep Neural Networks
• Training Deep Neural Networks with 8-bit Floating Point Numbers
• Scalable Methods for 8-bit Training of Neural Networks
• Post-training 4-bit quantization of convolution networks for rapid-deployment
• meProp: Sparsified Back Propagation for Accelerated Deep Learning with Reduced Overfitting
• A Study of BFLOAT16 for Deep Learning Training
• Trained Quantization Thresholds for Accurate and Efficient Fixed-Point Inference of Deep Neural Networks
• Bridging the Accuracy Gap for 2-bit Quantized Neural Networks (QNN)
• NICE: Noise Injection and Clamping Estimation for Neural Network Quantization
• Accelerating CNN Training by Pruning Activation Gradients